Entire solutions of quasilinear elliptic equations

We study entire solutions of non-homogeneous quasilinear elliptic equations, with Eqs. (1) and (2) below being typical. A particular special case of interest is the following: Let a be an entire distribution solution of the equation Delta(p)u = vertical bar u vertical bar(q-1)u, where p > 1. If q > p - 1 then u equivalent to 0. On the otherhand, if 0 < q < p - 1 and u(x) = o(vertical bar x vertical bar(p/(p-q-1))) as vertical bar x vertical bar -> infinity, then again u equivalent to 0. If q = p - 1 then u equivalent to 0 for all solutions with at most algebraic growth at infinity. (C) 2008 Published by Elsevier Inc.